Silicon-on-Insulator (SOI) structures are playing an increasingly important role in MOSFET technology, in particular, on account of their high working frequencies, low power losses, and low working voltages. Hitherto, the starting point has primarily been planar base substrates with an electrically insulating oxide layer and a thin active film. For recent component developments, it would be extremely advantageous if monocrystalline silicon regions which have an insulating layer, such as, for example, silicon oxide, around, or beneath them could be produced locally.